Leave it to the Astros, a team that's spent the last few years sending fans running to the record books, to the legal dictionary, and occasionally to the therapist, to be the team that in 2014 is sending us back to economics class.

Their general manager, Jeff Luhnow, has both an undergraduate business degree and a Kellogg MBA. Their assistant GM, David Stearns, came from the salary arbitration and collective bargaining team at MLB headquarters. Down the depth chart, their baseball operations analyst, Brandon Taubman, came from the derivatives trading world. Hell, their analogue of a traveling secretary (on this team a more comprehensive “manager of team operations”), Dan O’Neill, per his bio:

…spent seven years in the hedge fund industry with Mesirow Advanced Strategies, Inc. and as partner and chief operating officer of Oak Street Capital Management, LLC in Chicago, IL. Dan holds a B.A. from the University of Illinois and an MBA from the University of Chicago Graduate School of Business.

So it’s not at all a surprise that with the Jon Singleton contract this week, they were the team that was issuing the flashbacks to sitting in the back row of economics class.

And if I remember correctly, I was at the time the one playing the role of former Astro Bud Norris, who was critical of the deal that guaranteed Singleton $10 million but potentially did so at the expense of his upside.

1. The St. Petersburg Paradox and marginal value
Among several economics lessons that can be imparted from the Singleton extend-and-promote deal and the reaction to it is that of risk aversion. If you’re risk-neutral—in other words, you attach no value to certainty or to lowering the variance of your outcome—you’re on Norris’ side. You hate this deal. The expected return for Singleton, weighting all outcomes by their likelihood, is probably above what he is going to make.

I tried so hard to be risk-neutral. As a gambler, it’s a point of pride to figure expected values and go based solely on those. Hedging and other strategies to try to lower variance usually come at high cost. Ultimately, though, I was convinced that there is no such thing as being risk-neutral and that considering contracts like these on expected earnings is a silly way to go.

If you aren’t convinced, consider a game called the St. Petersburg Paradox, which has nothing to do with rationalizing the apparent impossibility that the Rays would have the worst record in the American League.

The game: I’m going to flip a coin. If it’s heads, you get $1 and the game ends. If it’s tails, I flip again. If it’s heads that time, you get $2 and the game ends, if it’s tails, I flip again. If it’s heads the third time, you get $4 and the game ends, if it’s tails, I flip again. And so on. $8, $16, $32…

How much would you be willing to pay to play that game?

No matter what you say, you’re picking something below the expected payout, which you may have known or figured out is infinity. 1*1/2 + 2*1/4 +4*1/8… = ½ + ½ + ½ +… forever.

If you’re willing to pay $100, you will almost certainly lose, even though the expected payout of the game beats yours. It’s an extreme case, but the point is that you don’t value those high ends nearly enough to make you want to figure the excesses of each step into your value of the overall bet. To you, it’s not a sum of ½ forever; it’s a sum that converges to something, since the value of that money to you isn’t really doubling at the end as the probabilities continue halving.

And that’s probably a better way to put Singleton’s situation. The second $10 million to somebody who already has $10 million isn’t worth anything close to what the first $10 million is. Depending on Singleton’s individual situation, there’s a good chance the next $20 million aren’t worth more than guaranteeing the $10 million. Possibly even the next $100 million. In other words, you’d rather have a guaranteed $10 million rather than coin flip for $110.

Dan Brooks yesterday conducted a poll that more resembled a so-called “can’t-miss” prospect’s situation, asking people whether they’d prefer $10 million guaranteed or a 5/6 chance at $25 million (expected value of $20.8 million).

The bigger the difference to you between the first $10 million and the marginal value of the next $10 million is, the smaller your chances of being a bust have to be to make it a good deal for the player to take.

2. Agents’ incentives and game theory
There are enough discussion points within this topic to fill a business school semester. The leverage aspect is one that has been much discussed, with Ben Lindbergh and Sam Miller talking on Effectively Wild about the rightness or wrongness of holding a promotion as a leverage tool against a player who hasn’t made much more than his $200,000 amateur draft signing bonus. And Mike Bates of SB Nation suggested ways of fixing this issue in collective bargaining.

But I wanted to go back to what Norris said, specifically the second half of his statement that he wished Singleton had listened to the union and not his agent.

Given everything just said about Singleton’s priorities and his valuation of money, it doesn’t seem at first like the agent would be driving any of those. Actually, it seems like he would be driving Singleton away from that deal. First of all, the agent’s cut isn’t significant money that would dwarf in importance any bigger payout with uncertainty in the future. Second, and building on the first point, the agent is wealthy, and this would hardly be that first money that guarantees his security.

Why the agent’s incentive is still to take the deal is probably just a guarantee of some business. The player can leave for a different agent any time he wants, and if that happens, the next one-year deal commission goes elsewhere. So in a way, the agent does get some certainty out of this, and does leave behind some potential upside. The risk factors are different—for the player, they’re underperformance and injury, and for the agent, it’s defection. But a players’ ability to change agents, while important and a basic right, is potentially costing players in this regard.

So to review, this is a deal that the player is in favor of, the agent is in favor of, and the union, which represents their interests, is presumably against.

And suddenly it’s back to economics class, this time a game theory application. The union doesn’t like this because in a world of perfect solidarity, these deals don’t happen. Nobody wants anybody else to take this deal because taking the deal waters down the pool. (Presumably, that is. There’s a case to be made that the few players who hit free agency will get more with so few players doing it, but on the whole it’s a believable argument.)

However, as in the prisoner’s dilemma, each individual could be better served by acting in his own interest no matter what anybody else is doing. It’s a little bit difficult to model, since the payoffs aren’t just money, as we saw in the first part of this. Payoffs also have to factor in certainty and other factors that are harder to measure.

So this will be an extreme oversimplification of an industry with dozens of agents and hundreds of players, boiled down to two participants in this dance—you and everyone else.

If everybody goes year to year, let’s say everybody gets 100 in value—just an arbitrary number. But the Jon Singletons of the world and their agents can get a lot of benefit from doing a cheap extension, so they can get up to 110 by doing that. However, that drives down prices, so the average player is hurt by it—by a much smaller amount, but hurt by it nonetheless.

So the chart might look like this, and again, the exact figures aren’t important.

Industry goes year-to-year

Industry does cheap extensions

You go year to year

You get 100, other players get 100

You do cheap extension

You get 110, other players get 98

It now looks like it’s everybody’s best move, assuming the industry has some standard of going year-to-year to deviate from that. But what happens if everybody deviates? Then the pain, if you’re a believer in Norris’ line of thinking, will start to be felt. Everyone’s payoffs drop by a larger amount in the new right column, where these become the norm.

Industry goes year-to-year

Industry does cheap extensions

You go year to year

You get 100, other players get 100

You get 80, other players get 92

You do cheap extension

You get 110, other players get 98

You get 90, other players get 90

The player’s side wants to be in that top left quadrant, where the industry-average payout is highest (100, 100). However, no matter which column we’re in, which is to say no matter what the rest of the industry is doing, if a player’s values prioritize security, he will be better off going year to year. It will in turn make the union as a whole a little worse off, but not enough to make what the player did worse for him.

(We see this sort of model in a lot of business cases, too. One classic example is overfishing the oceans, where the seas as a whole are suffering because everyone’s individual incentive, no matter what the industry is doing, is to overfish, whereas everybody would be better off if nobody overfished.)

Here, whether everybody else is “cooperating” or not, the player’s incentive is to do what’s best for himself and take the extension that offers the player security and the agent his payday. So the world ends up in the lower right quadrant, where everybody is making less (90, 90).

This oversimplified view of the baseball union maps out like a game of collusion, where everybody would be better off if there were an enforceable means of cooperating, which there really isn’t right now.

So what happens when the game is out of whack for one side? When an industry can’t get itself out of that lower right quadrant? The game often changes.

Who was the happiest when cigarette advertising on television was banned? It was actually the cigarette companies. In their game, if the competitors were advertising, it was in their best interest to advertise and not fall behind. If the competitors weren’t, it was in their best interest to advertise and blow them away. So advertising was a dominant strategy. Everybody spent a ton on advertising and sold the same cigarettes as they would have sold if nobody was. Once TV advertising was banned, they could just pocket that money and sell the same number of cigarettes. The rules of the game had changed.

A solution here isn’t so easy. Somehow preventing players from changing agents would get the agents’ priorities back in line with the union’s, but it doesn’t seem all that feasible. And if a player did truly want that security, the conflict would shift to player vs. agent rather than player/agent vs. union.

Maybe they do go that cigarette route and use the next round of CBA negotiations to use something that in the game theory sense, they can’t help themselves from taking. In his piece, Bates suggested not letting players with less than a year of service time sign extensions, which would be one approach.

But if enough people in the union leadership view the world like Norris—and his view is hardly unique—then understanding how the individual incentive outweighs the collective incentive could be as much of a focus as changing the leverage.